Volume 208, number 1,2 CHEMICAL PHYSICS LETTERS 4 June 1993
A set of f-polarization functions for pseudo-potential basis sets
of the transition metals SC-Cu, Y-Ag and La-Au
A.W. Ehlers, M. Biihme, S. Dapprich, A. Gobbi, A. Hijllwarth, V. Jonas, K.F. Kiihler,
R. Stegmann, A. Veldkamp and G. Frenking ’
Fachbereich Chemie, Universitiit Marburg, Hans-Meerwein-Strasse, W-3550 Marburg, Germany
Received 2 December I992
A set of seven-component f-type polarization functions has been optimized for use with the pseudo-potentials of Hay and Wadt
at the CISD level of theory for the transition metals SC-Cu, Y-A& La-Au in the energetically lowest-lying s’d” electronic state.
1. Introduction metals SC-Cu, Y-Ag and La-Au. The results are re-
ported in this study.
Because the computational efforts of ab initio cal-
culations increase rapidly with the number of elec-
trons, the core functions are often replaced by an ef-
fective core potential (ECP ) and in particular for
2. Theoretical methods
heavy atoms [ 11. Several sets of ECPs have been de-
veloped by various authors [ 2-91. We have recently
published [lo] a systematic test of the accuracy of The calculations have been performed using the
theoretically predicted geometries for transition metal Convex version of GAUSSIAN 92 [ 131. The va-
complexes using various ECPs with differently con- lence basis sets of the transition metals are derived
tracted valence shell basis sets. In this [ 101 and in from the (55/5/N) minimal basis sets #I optimized
other [ 111 studies we found that the geometries of by Hay and Wadt [ 31. We used the contracting
transition metal complexes in high oxidation states scheme (441/2111/(/V-1)l) with N=5 for the
can be calculated in good agreement with experi- first, N=4 for the second and N= 3 for the third row
ment at the Hartree-Fock (HF) level of theory using of the transition metals.
the (441/4l/(N-])I) or (441/2111/(N-1)l) The calculation of the f-polarization functions was
valence basis set developed by Hay and Wadt [ 31. carried out in two steps. First, the UHF [ 14 ] energy
For the calculation of energies, however, it was found was calculated for the s’d” state with the highest pos-
that additional f-type polarization functions may be- sible spin state which was monitored by Mulliken
come important [ 121. Since f functions were not population analysis [ 151. Then the energy was com-
available for the ECPs used in our studies [ lo- 121, puted using configuration interaction [ 161 with all
we optimized the exponents for seven-component f- CISD from the UHF reference determinant. The op-
type polarization functions for calculations using timal f exponents were obtained by numerical inter-
configuration interaction with single and double polation of the calculated atomic energiesat the CISD
substitution (CISD) in conjunction with the (441/
2 111/(N- 1) 1) valence basis set for the transition #’ This is not identical with LANLZMB implemented in
GAUSSIAN 92 [ 13 1. The latter has an additional p function for
the second- and third-row transition metals which is not given in
’ To whom correspondence should be addressed. ref. [3].
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved. 111
Volume 208, number I,2 CHEMICAL PHYSICS LETTERS 4 June 1993
levelusingthe (441/2111/(N-1)1/l) valenceba- that the “lanthanide-contraction” induces less dif-
sis set. fuse f functions for the elements Hf-Au. The values
for the f exponents decrease with increasing atomic
number within one group.
3. Results and discussion The UHF energies of the atoms at the electronic
state of highest multiplicity calculated with and
The optimized f exponents are summarized in ta- without additional f functions are summarized in ta-
ble 1. The values of the f exponents increase expo- ble 2. For the elements of the fourth and ninth triads
nentially within one period with increasing atomic (Cr, MO, W, Cu, Ag, Au) the calculated energies at
number. This trend is shown graphically in fig. 1. The the HF level do not change with an additional f func-
curve shows a hump for the first members of the tion. For the other elements the maximum energy
third-row transition metals because there is a jump lowering at the HF level is obtained for states with
in the atomic numbers between the first element La three unpaired and two unoccupied d electrons (Ti
(57) aad the second element Hf (72). It is obvious triad), and three paired and two unpaired d elec-
Table I
f exponents for the first-, second- and third-row transition metals
SC Ti V Cr Mn Fc co Ni cu
1.335 1.506 1.751 1.941 2.195 2.462 2.780 3.130 3.325
Y Zr Nb MO Tc Ru Rh Pd Ag
0.835 0.875 0.952 1.043 1.134 1.235 1.350 1.472 1.611
La Hf Ta W Re OS Ir Pt Au
0.591 0.784 0.790 0.823 0.869 0.886 0.938 0.993 1.050
O.CC@ I
3 4 5 6 7 8 9 10 II
Fig. 1. f exponents for the (0) first-, ( x ) second- and ( A ) third-row transition metals.
112
Volume 208, number 1,2 CHEMICAL PHYSICS LETTERS 4 June 1993
Table 2
UHF energies (au) with and without an f function for the lowest-lying s’d” state
SC Ti V Cr Mn Fc co Ni cu
-45.9233 1 - 57.48098 -70.67968 -85.65794 - 103.11747 - 122.53943 - 144.08356 -168.21291 - 194.99177
-45.92640 -57.48486 -70.68219 -85.65794 - 103.11983 - 122.54446 - 144.08868 -168.21582 - 194.99177
Y Zr Nb MO TC RU Rh Pd Ag
- 37.43 105 - 45.98220 -55.68176 -66.90180 -79.34132 -93.11322 - 108.68830 - 125.86224 - 144.89151
- 37.43349 -45.98580 -55.68432 -66.90180 -79.34416 -93.11925 - 108.69464 -125.86588 - 144.89151
La Hf Ta W Re OS Ir Pt Au
-30.77160 -48.23880 -57.09645 -67.09190 -78.27144 -90.18086 - 103.79734 -118.22716 - 134.53145
-30.77492 -48.24134 -57.09836 -67.09190 -78.27366 -90.18545 - 103.80232 -118.23013 - 134.53145
Table 3
CISD energies (au) with and without an f function for the lowest-lying s’d” state
SC Ti V Cr Mn Fe co Ni cu
-46.06083 -57.62669 -70.83266 -85.81021 - 103.28311 - 122.71083 - 144.27048 - 168.41605 - 195.20820
-46.92640 - 57.70846 - 70.93393 -85.92820 - 103.41409 - 122.85344 - 144.42268 - 168.57324 - 195.36717
Y Zr Nh MO Tc Ru Rh Pd Ag
-37.51863 -46.~7988 - 55.78320 - 66.99514 -79.44223 -93.21408 -108.78809 - 125.97978 - 145.00627
-37.57517 -46.15996 -55.88836 -67.12259 -79.59296 -93.38607 - 108.97758 -126.17735 -145.21811
La Hf Ta W Re OS Ir Pt Au
-30.85191 -48.32218 -57.18262 -67.17273 -78.36669 -90.28353 -103.89817 -118.31693 -134.61516
-30.91870 -48.38541 -57.26766 -67.27877 -78.50017 -90.43856 -104.07542 -118.51081 - 134.82628
0.m 1 i
3 4 5 6 7 8 9 10 II
Fig. 2. f exponents for the first-row transition metals compared to &electron calculations. (0 ) This work, ( A ) ref. [ 161, (0) ref.
[19], (0)ref. [20].
113
Volume 208, number I,2 CHEMICAL PHYSICS LETTERS 4 June 1993
trons (Co triad). The difference between the CISD References
energies with and without f functions listed in table
3 increases steadily from the early to the late tran- [ 1] L. Szasz, Pseudopotential theory of atoms and molecules
(Wiley, New York, 1985).
sition metals, La being an exception.
[2] P.J. Hay and W.R. Wadt, J. Chem. Phys. 82 (1985) 270,
It is interesting to compare the optimal f expo- 284.
nents for ECP wavefunctions with all-electron basis [3] P.J. Hay and W.R. Wadt, J. Chem. Phys. 82 (1985) 299.
sets. Bauschlicher and Walch [ 171 optimized a set [4] Y. Sakai, E. Miyoshi, M. Klobukowski and S. Huzinaga, J.
of f functions for Ti, Cr, Fe and Ni. They used a Comput. Chem. 8 (1987) 226,256.
[ 51 M. Dolg, U. Wedig, H. Stoll and H. Preuss, J. Chem. Phys.
Wachters [ 18 ] basis with two additional p functions
86 (1987) 866;
and a diffuse d function by Hay [ 191 contracted to D. Andrae, U. Haussermann, M. Dolg, H. Stall and H.
( 14~1lp6d)/ [6s6p3d]. These authors optimized the Preuss, Theoret. Chim. Acta 77 ( 1990) 123.
f functions by correlating the 4s, 3s, 3p and 3d elec- [6] J.C. Barthelat, P.K. Durand and A. Serafini, Mol. Phys. 33
trons at the CISD level. The values for the f expo- (1977) 159.
[ 7 ] L.G.M. Petterson, U. Wahlgren and 0. Gropen, Chem. Phys.
nents obtained in this manner are similar to our val-
80 (1983) 7.
ues for the pseudopotential basis set (fig. 2). [ 8 ] W.J. Stevens, M. Krauss, H. Basch and P.G. Jasien, Can. J.
The same authors [20] developed another set of Chem. 70 (1992) 612.
f functions for the same basis set contracted to [ 9 ] M.M. Hurley, L.F. Patios, P.A. Christiansen, R.B. Ross and
( 14~1lp6d)/ [ 5s4p3d] by optimizing the values of WC. Emler, J. Chem. Phys. 84 (1986) 6840.
[lo] V. Jonas, G. Frenking and M.T. Reetz, J. Comput. Chem.
Fe and Ni and selecting the values for the other ele-
13 (1992) 919.
ments by linear extrapolation. These values are [ 111 A. Veldkamp and G. Frenking, Chem. Ber., in press.
smaller than those of the less contracted basis set (fig. [ 121 A. Neuhaus, G. Frenking, C. Huber and J. Gauss, Inorg.
2). Dunning and co-workers [ 211 also developed a Chem., in press.
set off functions for the early transition metals of the [ 13 ] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill,
M.W. Wang, J.B. Foresman, B.C. Johnson, H.B. Schlegel,
first period using the same basis set contracted to
M.A. Robb, ES. Reploge, R. Gomberts, J.L. Andres, K.
( 14~1lp6d) / [ 5s4p3d]. These values are consider- Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J.
ably smaller, but the exponential increase is steeper. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople,
GAUSSIAN 92 (Gaussian Inc., Pittsburgh, 1992).
[ 141J.A. Pople and R.K. Nesbet, J. Chem. Phys. 22 ( 1959) 57 1.
[15] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833.
Acknowledgement
[ 16 ] J.A. Pople, J.S. Binkley and R. Seeger, Intern. J. Quantum.
Chem. Symp. 10 (1976) 1.
This work has been supported by the Fonds der [ 171 C.W. Bauschlicher Jr. and S.P. Walch, J. Chem. Phys. 76
Chemischen Industrie and the Deutsche Forschungs- (1982) 1033.
gemeinschaft. Additional support was provided by [IS] A.J.H. Wachters, J. Chem. Phys. 66 (1977) 4377.
[19] P.J. Hay, J. Chem. Phys. 66 (1977) 4377.
the HLRZ Jiilich, HHLR Darmstadt and the com-
[20] S.P. Walch and C.W. Bauschlicher Jr., J. Chem. Phys. 78
puter companies Convex and Silicon Graphics. ( 1983) 4597.
[21] B.H. Botch, T.H. Dunning Jr. and J.F. Harrison, J. Chem.
Phys. 75 (1981) 3466.
114
